Actually I googled "red budgie" and I found some pics but no relevant details.
Could they have been dyed?

From my understanding there is no such thing as a Red Budgie as Budgies do not have the required genetics to procude a red or pink mutation. A lot of things can dye a Budgie a red or pink colour such as mineral blocks, being fed specific coloured supplements mainly for red factor canaries or indeed people dying them colours.

Genetically you cannot have a red or pink budgie. In the colour spectrum there are 3 primary colours, Blue, Yellow and Red. All other colours are made from mixing the primary colours. The original colour of the budgie is green, which is a secondary colour and that is comprised of blue and yellow. We got blue budgies because the yellow gene went dormant in some birds.